Foundations of physics informed neural networks
Contact person: Kent-Andre Mardal
Keywords: Physics informed neural networks, constrained optimization
Research group: Mechanics
Department of Mathematics
Physics informed neural networks (PINNs) are algorithms where neural networks learn from data while at the same time are constrained by physics, most commonly described in terms of partial differential equations (PDEs). As such, PINNs gives raise to non-linear optimization problems constrained by PDEs. The mathematical foundation of PINNs is at precent under-developed as compared with traditional modeling methods such as finite element methods, but recent efforts hints towards a general framework also for PINNs. Applications in focus is biomechanical modeling of the brain, in particular in the context of the glymphatic system. Research proposals that address the foundations of constrained neural networks are welcome.
References:
[1] Karniadakis, George Em, et al. ""Physics-informed machine learning."" Nature Reviews Physics 3.6 (2021): 422-440.
[2] Zeinhofer, Marius, Rami Masri, and Kent-André Mardal. ""A Unified Framework for the Error Analysis of Physics-Informed Neural Networks."" arXiv preprint arXiv:2311.00529 (2023).
[3] Zapf B, Haubner J, Kuchta M, Ringstad G, Eide PK, Mardal KA. Investigating molecular transport in the human brain from MRI with physics-informed neural networks. Scientific Reports. 2022 Sep 14;12(1):15475." Partners are Simula Research Laboratory, University Hospital of Oslo
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